I am analyzing a 3-story building long 140m (X direction), wide 50m (Y direction) and high 13m. The interior spaces at the 2nd and 3rd floor are partitioned into modules of 7.2m by 9.6m defined by the structural grid, while at the 1st floor the interior space is partitioned in into modules of 7.2m by 4.8m due to the presence of auxiliary columns.
Beams in Y direction have reversed U-shaped cross section, while beams in X direction and columns have rectangular cross sections.
The building is modeled as follow:
- Columns and Beams are modeled with forceBeamColumn element, with fiber sections at the ends and elastic section in the middle. I used the HingeRadau integration technique.
- Columns at the first floor are fixed at the base
- Floor slabs are modeled as Rigid Diaphragm, and the master nodes are defined at each floor in the center of mass and they are able to move horizontally in X and Y directions, and to rotate around the Z axis (ops.fix(NodeTag, 0, 0, 1, 1, 1, 0))
- The rigid diaphragm prevents relative (in-plan) displacements between nodes of the same floor. In this case, the elongation/shortening of longitudinal
axis of the beam is prevented during the numerical analysis. Therefore, when the neutral axis of the RC cross-sections subjected to bending moment shifts because of cracking, the rigid diaphragm causes fictitious axial forces in the beam elements, thus overestimating the actual bending moment resistance and modifying the overall collapse mechanism. To avoid this numerical issue, an “axial buffer” has been introduced in the FE model. This element, that is assigned through a ZeroLength element object, is characterized by a virtually zero axial stiffness and very high stiffness in shear and bending. It is placed between one end of each beam and the adjacent node belonging to the rigid diaphragm, and it works as an axial release to eliminate the fictitious axial force.
- The mass of each floor is concentrated in the master node
I tried to perform non-linear static analyses in X and Y direction. Along the X direction the analysis converged, while in the Y it didn't converge and OpenSees gave me the following error message: "WARNING - ForceBeamColumn3d::update - failed to get compatible element forces & deformations for element: 303196(dW: << 2.54745e+06, dW0: 4.43317e+06)".
The message is related to one of the beam along Y direction, one of the elements with reversed U-shaped cross section.
To understand what was causing the problem I changed the reversed U-shaped cross section with a rectangular cross section and in this case the non-linear static analysis along Y direction converged.
I think there may be an incompatibility between the inverted U-shaped cross section and the ZeroLength element, but I can't figure out what it might be.
Does anyone have an idea what the problem might be?
Thank you in advance.
ZeroLength element - forceBeamColumn element interaction
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